2 2 Definitions and Biconditional Statements Definition Two

2. 2 Definitions and Biconditional Statements

Definition • Two lines are called perpendicular lines if they intersect to form a right angle. • A line perpendicular to a plane is a line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it.

Exercise • Decide whether each statement about the diagram is true. Explain your answer using the definitions you have learned. a. Points D, X, and B are collinear. b. AC is perpendicular to DB. c. <AXB is adjacent to <CXD. . A. D X . C . B

Biconditional Statement • Biconditional Statement – It is Saturday, only if I am working at the restaurant. • Conditional Statement – If it is Saturday, then I am working at the restaurant.

• Consider the following statement x = 3 if and only if x 2 = 9. a. Is this a biconditional statement? Yes a. Is the statement true? No, because x also can be -3.

• Rewrite the biconditional as conditional statement and its converse. – Two angles are supplementary if and only if the sum of their measures is 180°. – Conditional: If two angles are supplementary, then the sum of their measures is 180°. – Converse: If the sum of two angles measure 180°, then they are supplementary.

• State a counterexample that demonstrates that the converse of the statement is false. – If three points are collinear, then they are coplanar. – If an angle measures 48°, then it is acute.